If there is an Airmet for icing can you go through any clouds at all legally? Is a Airmet considered “known icing”? Are any clouds with a temp of 5 to -20c considered to have icing?
Is there a reliable method to determine thickness of clouds?
If Puget Sound area instrument-rated pilots could not climb through an overcast in winter we would essentially be grounded, and VFR-only pilots must choose their weather adventures wisely. Westerly winds bringing moisture-laden air into the Puget Sound basin bank ice-filled clouds against the west slopes of the Cascade Mountains, so VFR-only pilots bound for destinations east of the mountains can ask for "ice avoidance vectors" from ATC. When these are granted, instead of turning east toward the mountains these pilots are vectored west, over the Sound and lowlands, to climb above the freezing level before turning eastbound in clear air above the clouds. Something to consider after you complete your training: sometimes it is wiser to go in the "wrong" direction for a few miles in order to gain a large measure of safety.
I too have "thousands of hours," but that does not mean that I know everything. An AIRMET is a forecast.....how can that possibly be construed as "known,"?
It's a matter of definition. In that Bell letter linked above, the FAA explicitly defines "known icing" as being different from "known icing conditions". They also speak of "forecast icing conditions", which is defined in the AIM as "Environmental conditions expected by a National Weather Service or an FAA−approved weather provider to be conducive to the formation of inflight icing on aircraft." The most important sentence in the Bell letter is this: "If the composite information indicates to a reasonable and prudent pilot that he or she will be operating the aircraft under conditions that will cause ice to adhere to the aircraft along the proposed route and altitude of flight, then known icing conditions likely exist."
It's important to remember that AIRMETs cover wide ranges of area and several hours of time. You could see an AIRMET for icing covering an area hundreds of miles across when there is only a narrow band of icing working its way across that area over a period of 6 hours, but most of the time most of that area will be ice-free. As such, an AIRMET for icing is one (but not the only) factor in deciding if you're going to enter what is likely "known icing conditions" in violation of your aircraft's operating limitations. That's why it's important to use all available information to evaluate the potential for icing conditions to exist where you're flying, when you're flying as well as ways to avoid it along a given route.
Again, read that letter fully and carefully -- it's somewhat complex, but I think provides excellent insight into what the FAA will use to decide how to address an icing situation that comes to their attention.
As for the specifics of your question, if it's 11C at sea level, and the standard lapse rate is 2C per thousand feet, it's going to be about 1C at the 5000-foot cloud bases and colder in them. With the heart of the icing envelope being 0C to -10C, that's a situation ripe for structural icing. Also, in a non-FIKI airplane, any ice is too much, even if it's forecast light or even trace. I'd be more interested in the FIP Probability plots than the Severity plots, and if there's much chance at all of icing, I'd stay out of it without full FIKI equipment.
On the brighter side, you should also consider the thickness and coverage of the deck. With the breaks in the deck seen in your picture, it might not be hard to climb above the deck without entering those clouds. And even if you did brush through one and pick up some ice, given the amount of cloud-ground clearance, you'd have no problem descending back down to warmer air to melt it off. You might also find that with clear blue sunny skies above the deck, a bit of ice accumulated during a short brush with a cloud would be sublimated off by the radiant energy of the sun.
As for determining cloud height and tops, the most powerful tool I've found is the Cloud graphic Graphic Forecast for Aviation (GFA) tool on aviationweather.gov. It provides an excellent and in my experience generally reliable prediction of bases and tops as well as degree of cloud coverage. In combination with the other available tools such as the AIRMET Zulu, the FIP Probability charts, and Temperature Aloft forecasts, you can get a very good idea of where the icing is so you can plan to stay out of it.